## What is/are Bayesian Approach?

Bayesian Approach - We used multi-species occupancy models with a Bayesian approach to estimate bird occupancy.^{[1]}IUCNN contains functions to address specific issues related to the RL framework, including a regression-based approach to account for the ordinal nature of RL categories and class imbalance in the training data, a Bayesian approach for improved uncertainty quantification, and a target accuracy threshold approach that limits predictions to only those species whose RL status can be predicted with high confidence.

^{[2]}Genetic parameters were estimated using bivariate linear animal models under a Bayesian approach.

^{[3]}This is the first local study to apply a Bayesian approach.

^{[4]}The housing unit-level model is coupled with a probabilistic model of the heating and cooling system by using thermostat, power metre, and mechanical system catalogue data through a Bayesian approach.

^{[5]}In this manner, we construct a Bayesian approach to evaluating the posterior probability of various hypotheses given the observed states and actions of the robot.

^{[6]}In this work, for the robustness in wind resource assessment, we first propose a Bayesian approach in estimating Weibull parameters.

^{[7]}Both the Frequentist and Bayesian approaches show that in contrast to sham, active stimulation significantly reduced response times to peripherally presented low spatial frequency information.

^{[8]}The Bayesian approach has the advantage of providing an uncertainty quantification on the inferred source parameters.

^{[9]}In this paper, all models were estimated within the Bayesian approach.

^{[10]}In order to overcome this diculty, we employ a Bayesian approach by specifying a prior distribution for the variances of unique factors.

^{[11]}PurposeThis study proposes a Bayesian approach to analyze structural breaks and examines whether structural changes have occurred, at the onset of civil war, with respect to economic development and population during the period from 1945 to 1999.

^{[12]}A range of experimental data, both from this study and the literature, test the soundness of a Bayesian approach to modeling biomass hydrothermal carbonization kinetics.

^{[13]}Bayesian approach with posterior inference for change points was provided to know the particular change point that is optimal while Gibbs sampler was used to estimate the parameters of the change point model.

^{[14]}This contribution develops a Bayesian approach to the IP-detectability problem using decoupled transdimensional layered models, and applies an approach novel to geophysics whereby transdimensional proposals are used within the embarrassingly parallelisable and robust static Sequential Monte Carlo (SMC) class of algorithms for the simultaneous inference of parameters and models.

^{[15]}Relying on the latent class representation, we propose a Bayesian approach for estimation.

^{[16]}Moreover, to efficiently obtain reconstructions by minimizing a Tikhonov regularization functional (or alternatively, by computing the MAP estimator in a Bayesian approach), we develop an adjoint based scheme for gradient computation.

^{[17]}We focus here on Support Vector Machine (SVM) and Bayesian approaches, and our approaches are based on a cross-match with the Gaia catalog, which will eventually contain counterparts to virtually all stellar eROSITA sources.

^{[18]}We use a Bayesian approach where the solution to the inverse problem is given by the posterior distribution of the permeability field given the flow and transport data.

^{[19]}Following a Bayesian approach, the baseline and monitor seismic data are used in the seismic inversion to establish the regularized augmented function.

^{[20]}Nonlinear dynamic analysis is used to cover the actual nonlinear behavior of the structure in near-collapse performance level and the Bayesian approach to cover all uncertainties.

^{[21]}2 were further separately evaluated with a Bayesian approach.

^{[22]}This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow.

^{[23]}The approaches that have been reported so far can be mainly categorized into two classes: distance-based approaches and Bayesian approaches.

^{[24]}RESULTS To account for this correlated HP, we propose a Bayesian approach, MR-Corr2, that uses the orthogonal projection to reparameterize the bivariate normal distribution for γ and α, and a spike-slab prior to mitigate the impact of correlated HP.

^{[25]}The present work develops methods for inference of deterministic and aleatoric model parameters from noisy measurement data with explicit consideration of model discrepancy and additional quantification of the associated uncertainties using a Bayesian approach.

^{[26]}We closely followed the Bayesian approach to clarify the whole procedure in a logical order.

^{[27]}Therefore, the use of the Bayesian approach is important as an improved way of drawing statistical conclusions from clinical data since it facilitates the answer to the question, what is the probability that the effect is conclusive based on the data, which provides greater validity to the significant conclusions.

^{[28]}The tree of a subset of these sequences aligned with 247 publicly available sequences was reconstructed in spatio-temporal scale using the Bayesian approach, and the effective replication number (Re) was estimated using the birth-death model.

^{[29]}The Cox model with gamma frailty and Bayesian approach were used to determine the effective factors of frequent recurrences.

^{[30]}In fact, we impose priors on the sensitivity and the specificity scores corresponding to the members, taking a Bayesian approach.

^{[31]}With respect to the ranking results, significant differences are found between those generated from the proposed approach and those generated from the naïve ranking approach and a Bayesian approach based on the multivariate Poisson-lognormal model.

^{[32]}A Bayesian approach is developed to estimate and test moME effects and the corresponding effect sizes (ES).

^{[33]}In this work, we present the Bayesian approach for constructing a Gaussian process model.

^{[34]}For this purpose, we conducted a secondary data analysis of a large sample (2,217 participants) from eleven different, independent datasets with a Bayesian approach.

^{[35]}Thus, we propose a more comprehensive phylogenetic analysis using both parsimony and Bayesian approach, comprising 103 terminals of Cosmetidae, plus seven outgroup terminals scored for 130 morphological characters.

^{[36]}But alternative approaches were also proposed in the statistical literature, such as Bayesian approaches with Gaussian process models.

^{[37]}We use a Bayesian approach to estimate the transmission rates and local basic reproductive numbers of some urban mobility scenarios where residents of each patch spend daily the 100% (no human movement between patches), 75% and 50% of their day at their place of residence.

^{[38]}This paper proposes on the use of Bayesian approach to the composite Pareto models involving specification of the prior distribution on the proportion of data coming from the Pareto distribution, instead of assuming the prior distribution on the threshold, as often done in the literature.

^{[39]}Bayesian approaches that use computational modeling to quantify the level of uncertainty in a given result may provide a path towards improved confidence and use.

^{[40]}In the global isolate collection phylogeny, 34 clades were strongly resolved using Maximum Likelihood and Bayesian approaches (at >80% MLBS and >0.

^{[41]}To address this, we present a Bayesian approach for shrinkage of bounded wavelet coefficients in the context of non-parametric regression.

^{[42]}Probabilistic thresholds were defined using a Bayesian approach, finding the posterior probability of occurrence using the marginal and conditional probabilities of the control parameters along with the prior probability of occurrence of landslide.

^{[43]}

## maximum likelihood estimation

The Maximum Likelihood estimation method and the Bayesian approach using the Monte Carlo method by Markov Chains (MCMC) were used to find the parameters of the Gumbel distribution and the return levels were obtained for different periods.^{[1]}The statistical analysis is carried out using two different methods of parameter estimation: by maximum likelihood estimation and by Bayesian approach.

^{[2]}The Bayesian approach differs significantly from traditional statistical methods (first of all, it is focused on finding the most probable, rather than the only true value of the feature coupling coefficient), hence a graphical interpretation was provided for such basic concepts and techniques as probabilistic inference, maximum likelihood estimation and Bayesian confidence network.

^{[3]}EuroForMix and DNAStatistX are both based upon maximum likelihood estimation using a γ model, whereas STRmix™ is a Bayesian approach that specifies prior distributions on the unknown model parameters.

^{[4]}The maximum likelihood estimation and Bayesian approach were used.

^{[5]}

## maximum likelihood approach

Maximum likelihood approaches to inference using the EM algorithm and direct optimization of likelihoods are more frequently used, with Bayesian approaches being less favored due to computational demands.^{[1]}We use two approaches, the classical maximum likelihood approach and the Bayesian approach for estimating the distribution parameters and the reliability characteristics.

^{[2]}We use two approaches, the classical maximum likelihood approach and the Bayesian approach for estimating the distribution parameters and the reliability characteristics.

^{[3]}Unknown parameters, that are used to evaluate the measures of system effectiveness such as MTSF and steady-state availability, have been estimated by using maximum likelihood approach and Bayesian approach under different types of priors.

^{[4]}

## small sample size

We also argue for, and show an example of, how we by using a Bayesian approach can be more confident in our results and enable further studies with small sample sizes.^{[1]}BACkPAy is a pre-screening Bayesian approach to detect biological meaningful patterns of potential differential methylation levels with small sample size.

^{[2]}Methods: BACkPAy is a pre-screening Bayesian approach to detect biological meaningful clusters of potential differential methylation levels with small sample size.

^{[3]}Due to the small sample size, the individual corporate term structure is estimated by adding a positive parametric credit spread to the estimated Treasury term structure using a Bayesian approach.

^{[4]}

## measurement noise covariance

Then a novel variational Bayesian based event-triggered sequential measurement fusion (VB-ESMF) estimator is proposed to produce the local fused results of the clustered WSNs, where the variational Bayesian approach is used to infer the measurement noise covariance matrices of pseudo measurement noises.^{[1]}Each robot estimates its pose and measurement noise covariance matrices simultaneously in a decentralized manner based on the constructed hierarchical Gaussian models using the variational Bayesian approach.

^{[2]}Finally, the local optimal estimations of measurement noise covariance matrix and state are obtained by variational Bayesian approach.

^{[3]}

## 95 % credible

Hierarchical Bayesian approaches were used to estimate pooled incidence, progression, and 95% credible intervals (CrIs).^{[1]}Namely, the 95% credible interval in the Bayesian approach turns out to be 1.

^{[2]}Using a Bayesian approach, we calculate 95% credible interval upper limits of the gamma-ray flux and estimate limits on the cosmic-ray energy density of these regions.

^{[3]}

## mean square error

Results from the Bayesian approach produced lower impact estimate and lower mean square error compared with the classical approach.^{[1]}To circumvent the high root mean square error (RMSE) in the conventional AMP algorithm, a minimum mean square error (MMSE) denoiser is proposed based on the classic Bayesian approach and on the state evolution of AMP.

^{[2]}

## best linear unbiased

, pedigree-based best linear unbiased prediction (PBLUP), genomic-based best linear unbiased prediction (GBLUP), single-step GBLUP (ssGBLUP) and a non-linear Bayesian approach (notably BayesR).^{[1]},, pedigree-based best linear unbiased prediction (PBLUP), genomic-based best linear unbiased prediction (GBLUP), single-step GBLUP (ssGBLUP) and a non-linear Bayesian approach (notably BayesR).

^{[2]}

## Fully Bayesian Approach

Results With this fully Bayesian approach, associations between clinical measures and connectivity parameters emerge de novo from the data.^{[1]}A fully Bayesian approach was used to select the best explaining models and calculate their parameters.

^{[2]}This paper presents a fully Bayesian approach for lifetime prediction of anautomotive fleet using real workshop-service data as input.

^{[3]}Model estimation and the inference was fully Bayesian approach via integrated nested Laplace approximations (INLA).

^{[4]}As a fully Bayesian approach has been adopted, the functionalities are endowed with uncertainty quantification which is a crucial task in investigating unconventional reservoirs.

^{[5]}The model identifies countries with statistical evidence of SRB inflation in a fully Bayesian approach.

^{[6]}Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and predic- tion of cigarette demand at future time points using MCMC.

^{[7]}We tackle the current problem via a fully Bayesian approach based on a flexible statistical model named shifted-scaled Dirichlet mixture models (SSDMM).

^{[8]}This paper develops a fully Bayesian approach to adjust observed prevalence estimates for sensitivity and specificity.

^{[9]}Compared with the original RVM classification model, our proposed one is a Fully Bayesian approach, and it has a more efficient computation process.

^{[10]}Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method.

^{[11]}So it is reasonable to use a mixed method that combines a fully Bayesian approach and a wavelet basis.

^{[12]}While fully Bayesian approaches, such as those employing Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications.

^{[13]}We adopt the fully Bayesian approach for inference, prediction and model selection We discuss problems related to the estimation of degrees of freedom in the Student-t model and propose a solution based on independent Jeffreys priors which correct problems in the likelihood function.

^{[14]}Model parameters and inferences were based on a fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations.

^{[15]}Here, we developed methodologies with a fully Bayesian approach in discovering novel driver bio-markers in aberrant STPs given high-throughput gene expression (GE) data.

^{[16]}We adopt a fully Bayesian approach by assigning a transformed Gaussian Process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference.

^{[17]}Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of heterogeneous coefficients and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series.

^{[18]}A fully Bayesian approach is used to identify zones with high mortality risk in both a neighbourhood and its spatial lag (“high-high” clusters), and extended to identify recurring high risk clustering over more than one period.

^{[19]}

## Hierarchical Bayesian Approach

Hierarchical Bayesian approaches were used to estimate pooled incidence, progression, and 95% credible intervals (CrIs).^{[1]}In this letter, a hierarchical Bayesian approach is proposed for bias correction of the weather service surveillance radar (WSR-88D) dual-polarization (Dual-Pol) rainfall estimates in a hurricane.

^{[2]}In this paper, we present a hierarchical Bayesian approach to galaxy pitch angle determination, using spiral arm data obtained through theGalaxy Builder citizen science project.

^{[3]}Here, we propose a hierarchical Bayesian approach for control of a partially observable Markov decision process that enables conjoint learning of habits and reward structure in a context-specific manner.

^{[4]}Here we demonstrate the utility of the hierarchical Bayesian approach with application to a large compiled environmental dataset consisting of 5,741 marine vertical organic carbon flux observations from 407 sampling locations spanning eight biomes across the global ocean.

^{[5]}Using a hierarchical Bayesian approach, we estimated the number of cells required to be tested.

^{[6]}For this purpose, a Hierarchical Bayesian Approach (HBA) is applied to estimate the failure probabilities of each component while a Failure Mode, Effects and Criticality Analysis is performed to assess the severity.

^{[7]}Throughout this paper, we have adopted a hierarchical Bayesian approach, resulting in a single large probability distribution of all the parameters of all the galaxies, to ensure the most rigorous interpretation of our data.

^{[8]}For this purpose, a hierarchical Bayesian approach (HBA) was applied to estimate the failure probabilities of GRSs.

^{[9]}We present a hierarchical Bayesian approach for integrating failed captures and auxiliary encounter data in statistical capture-recapture models.

^{[10]}Using a hierarchical Bayesian approach, we estimated the number of cells required to be tested.

^{[11]}We propose SigTracer, a novel hierarchical Bayesian approach for analyzing intra-tumor heterogeneity based on mutation signatures to tackle these issues.

^{[12]}We first calibrated this system against plant trait and flux tower Net Ecosystem Exchange (NEE) using a novel emulated hierarchical Bayesian approach.

^{[13]}We develop a hierarchical Bayesian approach for the inference of large-scale spatial-temporal regression as often encountered in the analysis of imaging data.

^{[14]}We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution.

^{[15]}In this study, a hierarchical Bayesian approach is used to develop a predictive model for C T based on the reported C T values in the literature.

^{[16]}

## Novel Bayesian Approach

A novel Bayesian approach is developed to perform the estimation of model parameters in a reduced computational time.^{[1]}We propose a workflow, including a novel Bayesian approach, for estimating FAVs that combines measurements using direct and indirect methods and in silico values.

^{[2]}We propose a novel Bayesian approach that robustifies genomic modeling by leveraging expert knowledge (EK) through prior distributions.

^{[3]}As such, this data has the potential to underpin a novel Bayesian approach in the evaluation of clandestine laboratory evidence.

^{[4]}We propose a novel Bayesian approach combining Hamiltonian Monte Carlo with two likelihood approximation methods, namely, Euler approximation and Hermite expansion.

^{[5]}Here we introduce a novel Bayesian approach and nimbleCarbon, an R package that offers model fitting and comparison for population growth models based on the temporal frequency data of radiocarbon dates.

^{[6]}To this end, we developed a novel Bayesian approach that simultaneously estimates diversification-rates through time from time-calibrated phylogenies and correlations between environmental variables and diversification rates.

^{[7]}A novel Bayesian approach was used in addition to the classical hypothesis testing during data analyses.

^{[8]}These uneven weights to different nodes are assigned by taking a novel Bayesian approach to the problem where the problem of learning for each device/node is cast as maximizing the likelihood of a joint distribution.

^{[9]}This paper proposes a novel Bayesian approach capable of jointly estimating the pulse location; interpolating the almost annihilated signal underlying the strong discontinuity that initiates the pulse; and also estimating the long pulse tail by a simple Gaussian Process, allowing its suppression from the corrupted signal.

^{[10]}This letter presents a novel Bayesian approach for unsupervised SPM of hyperspectral imagery (HSI) based on the Markov random field (MRF) and a band-weighted discrete spectral mixture model (BDSMM), with the following key characteristics.

^{[11]}

## Variational Bayesian Approach

Then a novel variational Bayesian based event-triggered sequential measurement fusion (VB-ESMF) estimator is proposed to produce the local fused results of the clustered WSNs, where the variational Bayesian approach is used to infer the measurement noise covariance matrices of pseudo measurement noises.^{[1]}Due to the negative effects of the nonlinearity and latent variables on parameter estimation, the model is estimated using a variational Bayesian approach.

^{[2]}In this study, we develop a variational Bayesian approach for real-time estimation of noise covariance and nodal water demands.

^{[3]}Based on the new model and utilized the random matrix framework, a variational Bayesian approach is derived, which recursively and efficiently estimates kinematic and extension states.

^{[4]}Each robot estimates its pose and measurement noise covariance matrices simultaneously in a decentralized manner based on the constructed hierarchical Gaussian models using the variational Bayesian approach.

^{[5]}To obtain approximate posteriors of the hidden variables, a variational Bayesian approach is proposed.

^{[6]}Latent nodal attributes are estimated via a variational Bayesian approach and may change over time, representing natural shifts in network activity.

^{[7]}Finally, the local optimal estimations of measurement noise covariance matrix and state are obtained by variational Bayesian approach.

^{[8]}

## Proposed Bayesian Approach

Methods: A new proposed Bayesian approach was applied for assessing functional response to emotional musical auditory stimuli in a block design fMRI data with 105 scans of two healthy and depressed women.^{[1]}We show that the proposed Bayesian approach performs well in fitting and forecasting Japanese mortality.

^{[2]}The proposed Bayesian approach using the delayed rejection and adaptive Metropolis (DRAM) algorithm was compared with the Metropolis-Hastings (MH) algorithm in the uncertainty estimation of Weibull distribution parameters.

^{[3]}The proposed Bayesian approach hence improves IVIM parameter estimation in brain cancer and acute stroke.

^{[4]}Conclusions The proposed Bayesian approach with reasonable prior information improved estimates of influenza-associated disease burden.

^{[5]}The proposed Bayesian approach uses a Hamiltonian Monte Carlo-within-Gibbs technique to fit smoothing splines to the spatial periodogram.

^{[6]}The proposed Bayesian approach in this study gives the updated distributions of ch from a limited number of test data and recommends model M2 for calculating ch.

^{[7]}The proposed Bayesian approach allows (1) the localization of the defect, and (2) the identification of different candidate damage hypotheses and their ranking based on probabilities that measure their relative degree of belief.

^{[8]}

## New Bayesian Approach

In this paper, a new Bayesian approach is proposed to extend offline RPD to online multi-response RPD by making full use of this additional information.^{[1]}This new Bayesian approach also allows the within-individual variability to differ for each individual, compared to other less flexible approaches.

^{[2]}Therefore, we study a new Bayesian approach to developing thinking machines using Bayesian decision theory.

^{[3]}This paper deals with a new Bayesian approach to the two-sample problem.

^{[4]}Recently, a new Bayesian approach was developed for brain imaging and evaluation of perfusion indexes (Kudo et al.

^{[5]}This paper presents a new Bayesian approach to equation discovery – combined structure detection and parameter estimation – for system identification (SI) in nonlinear structural dynamics.

^{[6]}We proposed a new Bayesian approach to estimate continuous crustal strain-rate fields from spatially discrete displacement-rate data, based on Global Navigation Satellite System (GNSS) observations, under the prior constraint on spatial flatness of the strain-rate fields.

^{[7]}

## Parametric Bayesian Approach

Lacking informative or historical knowledge of the parameter, a parametric Bayesian approach cannot be expected in complex statistical problems.^{[1]}This article introduces Targeted Smooth Bayesian Causal Forests, or tsbcf, a semi-parametric Bayesian approach for estimating heterogeneous treatment effects which vary smoothly over a single covariate in the observational data setting.

^{[2]}In this work we present a non-parametric Bayesian approach for developing structure-property models for grain boundaries (GBs) with built-in uncertainty quantification (UQ).

^{[3]}In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression.

^{[4]}Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in par